The line which we needed is perpendicular to a line whose slope is `(-3/2)` .
the product of the slopes of two lines which are perpendicular is equal to `-1`
let the slope of the line which we need to find be `m_1` and the slope of the other line be `m_2 = (-3/2).`
`m_1 * m_2 = -1`
=> `m_1 = -1/(m_2) = -1 /(-3/2) = 1/(3/2) = 2/3`
so , `m_1 = 2/3`
and the line of slope `m_1` passes through the point `(-4,1)`
then the line is
`y = mx+c`
=> `y = (2/3)x +c`
as it passes through `(x,y)=(-4,1)` so
=> `1= (2/3)(-4) +c`
=>` 1= -8/3 +c`
=> `1+8/3 = c`
=> `c = 11/3`
so the equation of the line is `y= (2/3)x+ 11/3` and the graph plotted is as follows in the attachments. the point `(-4,1)` is spotted with a green dot.